The Time Domain Plot Shown Below Comes From 50 000 Values Recorded Every 2

8/21/2019 The Time Domain Plot Shown Below Comes From 50 000 Values Recorded Every 2

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EN5500

ENGINEERING ANALYSIS 3

PART A: SIGNAL PROCESSING

April 2014

Arnaud GIRIN 0616470


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Table of Contents

1 Introdut!on"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""1

1"1 T!#e do#a!n s!$nal %lot""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""1

1"& 're(uen) do#a!n %lot""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""1

& Set!on 1"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""&

&"1 S!$nal %roess!n$ tool"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""&

&"& T*e t!#e do#a!n %lot + Set!on 1""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""3

&"3 're(uen) do#a!n %lot + Set!on 1""""""""""""""""""""""""""""""""""""""""""""""""""""""""""",3 Set!on & and 3""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""",

3"1 T!#e do#a!n s!$nal - Set!on &""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""".

3"& 're(uen) do#a!n - Set!on &""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""".

3"3 T!#e do#a!n s!$nal - Set!on 3"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""/

3", 're(uen) do#a!n - Set!on 3"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""/

, at*lab Code""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

5 2!suss!on and onlus!on"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""10


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L!st of $ures

'!$ure 1: T!#e do#a!n s!$nal %lot""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""1

'!$ure &: 're(uen) do#a!n %lot""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""1'!$ure 3: T!#e do#a!n %lot - Set!on 1""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""3

'!$ure ,: 're(uen) do#a!n %lot for set!on 1""""""""""""""""""""""""""""""""""""""""""""""""""""""",

'!$ure 5: Plot of t!#e do#a!n s*o4!n$ t*e last alue aboe t*e set u% t*res*old" 5

'!$ure .: Set!on & T!#e do#a!n s!$nal""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""".

'!$ure /: Set!on & 're(uen) do#a!n""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""".

'!$ure : Set!on 3 T!#e do#a!n s!$nal"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""/

'!$ure 6: Set!on 3 're(uen) do#a!n"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""/

'!$ure 10: 're(uen) do#a!n o#%ar!son %lot""""""""""""""""""""""""""""""""""""""""""""""""""""10


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1 Introdut!on

T*e ob7et!e of t*!s stud) !s to de#onstrate t*e e8et of utt!n$ out data on a

s!$nal fre(uen) do#a!n"

9s!n$ t*e $!en readls$lEn$&01,"# ode t*e t!#e do#a!n s!$nal %lot and

fre(uen) do#a!n %lot an be obta!ned fro# t*e A1010000"b!n Lab!e4 le"

Cr!ter!on are to be set u% to dene t*res*old so t*at t*e data an be s%l!tted !n 3

set!ons"

1"1 T!#e do#a!n s!$nal %lot T*e t!#e do#a!n %lot s*o4n belo4 o#es fro# 50 000 alues reorded eer)

2×10−7

seonds dur!n$ a %er!od of 0"01 seond ;5


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& Set!on 1

&"1 S!$nal %roess!n$ tool

Set!on 1 !s t*e %art of t*e t!#e do#a!n s!$nal before t*e s!$nal $ets s!$n!ant

alues" T*!s %art *as t!n) ?utuat!ons for about s ;about 1000 %o!nts>" T*e

atlab s!$nal %roess!n$ tool !s used to =oo# !n to t*!s set!on" 9s!n$ t*e ert!al

and *or!=ontal #ar@ers t*e #a!#u# alues are deter#!ned"

a!#u# alues for set!on 1:

At %o!nt &6/: ) B -0"01..5&3&

At %o!nt .56: )B 0"01505,,6

T*e *!$*est alue of t*ese t4o $ures ;)B0"01505,,6> #a@es t*e u%%er and

lo4er ;-)> t*res*old for set!on 1 %ro$ress!n$ to4ards *!$*er alues of t!#e t*erst alue aboe t*!s alue !s assu#ed to belon$ to t*e net set!on"

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T*e t!#e do#a!n ar!able onta!n!n$ 50 000 alues !s t*en ut out at t*e 6,t*

alue 4*!* orres%ond to t*e last alue 4!t*!n t*e set l!#!t"

T*e atlab o##and to ut t*!s ar!able at t*e re(u!red alue and %ut !t !nto a

ne4 ar!able !s:

)s1B);1:6,>

T*e ar!able )s1 ;s1: Set!on1> !s reated and onl) onta!ns t*e 6,t* alues of

t*e #a!n ar!able"

A s!#!lar o%erat!on !s #ade to $enerate su!table a!s alues:

s1B;1:6,>

&"& T*e t!#e do#a!n %lot + Set!on 1

Figure !: Time domain plot " #ection 1

To %lot t*e orres%ond!n$ fre(uen) do#a!n t*e follo4!n$ atlab o##and !s

used:

D%))s1f B %4el*;)s1DD,06.fs>

T*e funt!on reates t4o ar!ables:

)))s1 !s t*e ) alues ar!able of %o4er s%etral dens!t)"

f !s t*e $enerated fre(uen) ran$e

It an not!ed t*at t*e o%t!ons for t*!s funt!on are @e%t t*e sa#e t*an !n t*e

readls$lEn$&01,"# ode t*e onl) *an$!n$ !n%ut !s )s1"

F*en reat!n$ t*e %lot for t*e fre(uen) do#a!ns t*e t4o ar!ables %))s and f

;4*ere !s t*e set!on nu#ber> are redued to alue belo4 110. " T*!s *el%s to el!#!nate t*e !ns!$n!ant

alues for t*e fre(uen) %lot"

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&"3 're(uen) do#a!n %lot + Set!on 1

Figure 4: Frequenc domain plot $or section 1

3 Set!on & and 3

Set!on & !s surrounded b) set!on 1 and 3" T*e rst one *as been deter#!ned so

t*e net ste% !s to establ!s* a su!table t*res*old to ut out set!on 3 so t*at onl)

t*e s!$n!ant alues for set!on & are @e%t for furt*er stud!es"

T*e *osen t*res*old !s based on a S!$nal to No!se of 100 ;&0dH> 4*!* #eans

t*at t*e t*res*old !s set at 1 of t*e #a!#u# a#%l!tude reorder for t*e s!$nal"

In t*!s ase t*e #a!#u# a#%l!tude for t*e ent!re s!$nal !s 3"0&63 ;t*!s alue !s

s*o4n on t*e atlab ar!able 4!ndo4s at t*e orres%ond!n$ ro4>" T*e u%%ert*res*old !s t*erefore set to 0"030&63 and t*e lo4er one to -0"030&63"

T*e &6361t* alue !s t*e last alue oer t*e set t*res*old"

,


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Figure %: &lot o$ time domain s'o(ing t'e last )alue a*o)e t'e set up t'res'old

Jno4!n$ t*!s alue t*e set!on & and 3 an be reated !n t4o d!8erent ar!ables

)s& and )s3 ;4!t* orres%ond!n$ s& and s3 a!s alues>"

9s!n$ t*e %4el* funt!on t*e fre(uen) do#a!ns of t*ese t4o re#a!n!n$

set!ons an be deter#!ned"

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3"1 T!#e do#a!n s!$nal - Set!on &

Figure 6: #ection 2 Time domain signal

3"& 're(uen) do#a!n - Set!on &

Figure 7: #ection 2 Frequenc domain

.


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3"3 T!#e do#a!n s!$nal - Set!on 3

Figure +: #ection ! Time domain signal

3", 're(uen) do#a!n - Set!on 3

Figure ,: #ection ! Frequenc domain

/


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, at*lab Code

%==========================================================================

%==========================================================================

% Matlab m-files: Frequency_Domain_Section_1_2_3.m

% Autor: Arnau! "#$#

% Date: 2& A'ril 2(1)

% *sa+e:

% - ,is routine uses it a function rea!l/s+l_M0n+_2(1).m

% - *ses te +enerate! an! y /ariables

% - uts out te /ariable into 3 sections accor!in+ to 're!efine! tresol!

% - ut'ut /ariables: s1 s2 s3 ys1 ys2 ys3 'yys1 'yys2 'yys3

% - *ses 'elc function to turn te time !omain /ariable into frequency!omain

% - 4lot +ra's of te time an! frequency !omain for te tree sections

% - 4ut tis routine an! rea!l/s+l_M0n+_2(1).m in a matlab5s !efault fol!er

6or7s8 or a!! anoter 'at

%==========================================================================

rea!l/s+l_M0n+_2(1)9

ys1=y61:&)89

s1=61:&)89

ys2=y6&):2&3&189

s2=6&):2&3&189

ys3=y62&3&1:;((((89

s3=62&3&1:;((((89

%Section 1 time an! frequency !omain 'lots

fi+ure


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'lot6s1ys18

label65,ime 6s858

ylabel65Am'liture 6>)(&?fs89

f=f61:218

'yys1='yys161:218

fi+ure

'lot6f'yys18

title65Frequency !omain - Section 158

label65Frequency 6@858

ylabel654oer s'ectral !ensity58


fi+ure

'lot6s2ys28

label65,ime 6s858


f=f61:218

'yys2='yys261:218

fi+ure

'lot6f'yys28




6


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fi+ure

'lot6s3ys38

label65,ime 6s858


f=f61:218

'yys3='yys361:218

fi+ure

'lot6f'yys38




10


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5 2!suss!on and onlus!on

Ea* fre(uen) do#a!n %lot seen on t*!s stud) o#es 4!t* t*e *!$*est alue fort*e ent!re %lot !t an be seen t*at t*e *!$*est alue for set!on & ;&"1.&10 -5> !s

t4!e as b!$ as for set!on 1

;,"&110-6> and 3 ;."31.1010>"

oreoer t*e fre(uen) %ea@s for ea* set!ons are so#et!#es s!#!lar or lose

to ea* ot*er t*!s s!$nal %roess!n$ %art *el% to %ur$e t*e unneessar) data

t*at ould lead to error"

T*e $ure belo4 s*o4s t*e d!8erenes !n a#%l!tudes a$a!nst fre(uen) of bot*

t*e ent!re s!$nal ;%)) !n blue> and t*e set!on & s!$nal ;%))s&>"

Figure 10: Frequenc domain comparison plot

T*e ut of t*e a%%ro%r!ate set!on *as #ade t*e %o4er s%etral dens!t) *!$*erfor set!on & t*an t*e ent!re s!$nal" El!#!nat!n$ un4anted data #a@es t*e data

#ore aurate and eas) to stud)"

T*!s %roes t*e !#%ortane of selet!n$ t*e r!$*t set!on for t*e des!red data to

be stud!ed"

an) ot*er t*res*old r!ter!a ould *ae been used su* as us!n$ set!on 1

t*res*old for set!on 3 t*res*old" Also t*e atlab s!$nal %roess!n$ tool ould

*ae been run 4!t* ert!al #ar@ers 4!t* tra@!n$ and slo%e to use an an$ular

r!ter!a for a t*res*old"

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1&

The Time Domain Plot Shown Below Comes From 50 000 Values Recorded Every 2

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